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Asymptotic behaviour of logistic regression [duplicate]

Assume that we use logistic regression with a given regression function r(x) for each sample vector x. Is is true that if we have infinite samples, we have r(x) = log(p(x)) - log(q(x)) where p(x) is ...
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Bias and variance of coefficient estimation of logistic regression

For a linear regression problem $y=X\beta + \epsilon$, I think we know very well that the estimated $\hat{\beta} = \dfrac{X^Ty}{X^TX}$ is unbiased, and has the variance introduced by $\epsilon$. It ...
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Does there exist an analogous statement to BLUE (Gauss-Markov) for GLMs?

I recall from my graduate school days that the Gauss-Markov (GM) theorem states that the Best Linear Unbiased Estimator (BLUE) in a linear regression is $\vec{\beta}=(X^TX)^{-1}X^T\vec{y}$. An amazing ...
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819 views

Sampling/Asymptotic Distribution of Estimated Coefficients of Logistic Regression

If I understand correctly, in a logistic regression, we have that $Y_i \mid X \sim Bern(S(X\beta))$ where $S(x)$ is the sigmoid function. Suppose we estimate $\beta$ using MLE and get $\hat \beta$. ...
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417 views

Partially Full Factorial Logistic Regression - Bias?

I have an "partially" full factorial designed experiment (3 factors) that looks like this (both VAR1 and VAR2 are numeric factors): As you can see, Population A and B share all of VAR2 levels and the ...
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230 views

I'm playing with some Monte Carlo simulations to get an idea of the properties of some linear and non-linear models. The linear OLS model in my case is specified as: $Y_t = \beta_0 + \beta_1x+ \... 4 votes 1 answer 92 views Should I use regularization in a price elasticity model? I am building a price elasticity model using linear regression: log(demand) ~ 1 + log(price) + ... Does it make sense to use L1 and/or L2 regularization to prevent ... • 1,086 1 vote 1 answer 106 views Does this formula hold for the coefficients of a logistic regression$\pmb{\hat{\beta}} \sim N(\pmb{\beta}, (\mathbf{X}^T\mathbf{X})^{-1}\sigma^2)\$? [duplicate]

A person on Cross Validated states that the coefficients of the general linear model follows the following distribution $$\pmb{\hat{\beta}} \sim N(\pmb{\beta}, (\mathbf{X}^T\mathbf{X})^{-1}\sigma^2)$$ ...
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1 vote
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Logistic Regression Simulation Apparent Bias

Hi Other Stats Humans! I am simulating some data and I am observing some unexpected results. After simulating the data, I found that when the true odds ratio is less than one, the estimated odds ...
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